Fibonacci Numbers — Count the Spirals on a Pinecone

In 1202 Leonardo of Pisa -- Fibonacci -- wrote down a sequence where each number is the sum of the two before: 1, 1, 2, 3, 5, 8, 13, 21... The astonishing thing is that plants count with these numbers, and you can check it yourself.

Take a pinecone (a sunflower head or a pineapple works too). Look at the base: the scales form spirals winding one way and another set winding the other way. Mark a starting scale and count the spirals going clockwise, then count those going anticlockwise. Write both numbers down.

Your two spiral counts are almost always two numbers that sit next to each other in the Fibonacci sequence -- very often 8 and 13, or 5 and 8, or 13 and 21. Check them against the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34. Plants grow this way because it packs the seeds most efficiently.

What is true and what is exaggerated. (1) Fibonacci spiral counts in pinecones, sunflowers, pineapples and daisy petals are REAL, and happen because each new part grows at the 'golden angle' of about 137.5 degrees, which packs them tightest. (2) The ratio of neighbouring Fibonacci numbers genuinely approaches the golden ratio, phi = (1 + square root of 5) over 2 = 1.618..., the number satisfying phi-squared = phi + 1. (3) But be sceptical of claims that the golden ratio rules the Parthenon, the Mona Lisa or the 'perfect' face -- many are cherry-picked or made up. The maths in the pinecone is beautiful and real; not every romantic story about it is.